I would be very grateful if someone could help me date both the vase and the signature pictured in the images below. As far as I can tell, it looks like a famille rose, meiping-type vase, but I'm still clueless as to the approximate era in which it was made.

Your vase is Japanese made by the Fukagawa Koransha company.
Above the seal mark is the Koransha orchid.
I think the marks is the same as the one in my picture below.
According the Koransha website this mark is from Showa 10 (1935) till the end of WWII (1945).
Regards,
Martin.

Firstly your vase is Japanese and not Chinese.
The blue orchid mark is the Fukagawa mark. Earlier designs had the iron red orchid.
Your vase dates from early 20th century onwards.
The company is still owned and operated by family members.
It came under Royal patronage in 1910.
A nice example.
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